Your appointment letter can be taken as a contract between you and your employer. Hence, it is up to the employers discretion to reserve the full notice period as provided in the Letter of Appointment.
So to answer your queries:
1. Can my employer hold my last month's salary and Full & Final Settlement? I have already asked them to recover the balance notice period from my leave encashment, amount of leave encashment is higher than the recovery amount.
---The company has to agree to your notice period "buy out" offer. Often companies prefer Man-hours than monetary compensation to find suitable replacement of a discharged employee in the meanwhile. So they can hold your last months salary or full and final settlement until the expiration of the predefined notice period or anything otherwise mutually agreed between you and your employer in response to your application for an early release.
2. Can my employer hold the Relieving Letter?
-Relieving letter is provided on the last day of service with an organization, so the possibility mentioned above holds good for this as well.
3.Can my employer hold the Relieving Letter?
Yes you can, but the merit will be in your favor only when your employer doesn't release the FnF settlement and Relieving letter even after the expiration of your contracted notice period or as agreed by your company.
4.Can my employer take any legal action against me for not serving full notice period?
--It is a violation of contract, hence they can. But in practical situations, the employers generally try to negotiate to secure their interests within the provisions of the contract and withhold the release documents. But they can if they wish to.
5. Can my current employer take any legal action against my new employer for hiring me since they have not issued any Relieving Letter. Please note my current employer doesn't require any Relieving Letter from my present employer, an undertaking will be sufficient for them.
--Since the new employer has merely extended an offer of employment that you possibly may have accepted, hence the liability rests on you and not with your new employer added by the fact that they will obtain an undertaking from you at the time of joining.
Companies can take release letters at a later date for early joining according to the extent defined in your undertaking.
Hope this clarifies.